Is it a sin for someone to deliberately make another person swear to a lie in order to take revenge on them?

It is not permissible to administer an oath to a person whom you know will lie in his oath, unless there is a significant benefit related to establishing a right or refuting an accusation. This is because it trivializes the oath and causes the swearer to fall into a grave sin. This is something we have been forbidden from, so do not be an aid to Satan against your brother.